Direct measurement of the scattering cross sections of liquid ortho-deuterium for ultracold neutrons and comparison with model calculations

Liquid deuterium is a fluid between the quantum and classical regimes. It attracts interest from fundamental research for the verification of quantum calculations but also from neutron physics as it is a widely used neutron moderator medium. We have measured the scattering cross sections of liquid ortho-deuterium in the ultracold-neutron range for four different temperatures (19–23 K) and compared them with calculations from a parameter-free analytical calculation model as well as with previous measurements at 19 K by another research group. All three show remarkable agreement, which establishes the validity of the calculation model and proves it is a reliable basis for the derivation of scattering kernels. The deconvolution of our measured transmission data changed the cross-section results noticeably only for neutrons faster than 10 m/s. We found the total scattering cross section of liquid deuterium to be inversely proportional to velocity, as is predicted by theory.

Figure 1

The TOF geometry of the UCN transmission measurements on liquid ortho-deuterium.

Figure 2

Experimental data points (solid colored symbols) for the scattering cross sections of liquid ortho-deuterium at various temperatures. The theoretical model by Döge et al. [18] was calculated for the same temperatures as in this experiment using $c_{\text{ortho}}=0.972$ (solid colored lines) and the self-diffusion coefficient for liquid deuterium from O'Reilly and Peterson [39]. The temperature uncertainty in the experiment was $\mathrm{\Delta }T=\pm 0.25$ K. The total cross-section data from Atchison et al. [15] are shown for comparison (PSI 2005, yellow stars) and match both our measured data and the calculation model well. Our scattering cross sections were corrected for absorption on ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, and the Atchison et al. data were not. This correction falls within the error bars and is thus negligible.